On Packing Low-Diameter Spanning Trees
Julia Chuzhoy, Merav Parter, Zihan Tan

TL;DR
This paper investigates the existence and bounds of low-diameter spanning tree packings in highly connected graphs, providing new theoretical bounds and demonstrating their near tightness, with applications in distributed computing.
Contribution
It introduces the first non-trivial upper and lower bounds on the diameter of tree packings in edge-connected graphs, advancing understanding of their structure and applications.
Findings
Existence of tree packings with diameter bounds depending on graph parameters
Probabilistic methods yield packings with controlled diameter and congestion
Results are nearly tight, showing fundamental limits of low-diameter packings
Abstract
Edge connectivity of a graph is one of the most fundamental graph-theoretic concepts. The celebrated tree packing theorem of Tutte and Nash-Williams from 1961 states that every -edge connected graph contains a collection of edge-disjoint spanning trees, that we refer to as a tree packing; the diameter of the tree packing is the largest diameter of any tree in . A desirable property of a tree packing, that is both sufficient and necessary for leveraging the high connectivity of a graph in distributed communication, is that its diameter is low. Yet, despite extensive research in this area, it is still unclear how to compute a tree packing, whose diameter is sublinear in , in a low-diameter graph , or alternatively how to show that such a packing does not exist. In this paper we provide first non-trivial upper and lower…
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